Defects extremal surfaces and interface CFTs

We propose a generalization of the defect extremal surface (DES) prescription to holographic interface conformal field theories (ICFTs), extending its applicability beyond the AdS$_3$/BCFT$_2$ framework. We consider a holographic ICFT$_2$ comprising two CFT$_2$s coupled across an interface, dual to two asymptotically AdS$_3$ geometries joined by a codimension-one end-of-the-world (EOW) brane. In the corresponding effective lower-dimensional description obtained via partial dimensional reduction on the brane-boundary combination, the theory on the brane is coupled to gravity, thereby enabling the computation of fine-grained entanglement entropy via the island formula. We demonstrate that the generalized DES prescription exactly reproduces the effective lower-dimensional results for finite subsystems in time-independent scenarios in the large brane tension limit, corresponding to weak gravitational coupling on the EOW brane. We further compute the entanglement entropy of semi-infinite bipartite pure states in radiation subsystems coupled to $2d$ eternal black holes, and obtain the corresponding Page curves.